Does the scale-free topology favor the emergence of cooperation?

TL;DR

This study investigates how the structure of scale-free networks influences the emergence and stability of cooperation in evolutionary prisoner's dilemma games, revealing that dynamics significantly affect outcomes.

Contribution

It provides a detailed analysis of cooperation dynamics on scale-free networks, highlighting the impact of different update rules on cooperation persistence.

Findings

Cooperation levels depend strongly on game dynamics.

A phase transition from coexistence to defection occurs under certain conditions.

Network topology alone does not guarantee cooperation stability.

Abstract

In a recent Letter [F.C. Santos and J. M. Pacheco Phys. Rev. Lett. \textbf{95}, 098104 (2005)], the scale-free networks are found to be advantageous for the emergence of cooperation. In the present work an evolutionary prisoner's dilemma game with players located on Barab\'asi-Albert scale-free networks is studied in detail. The players are pure strategist and can follow two strategies: either to defect or to cooperate. Serval alternative update rules determining the evolution of each player's strategy are considered. Using systematic Monte Carlo simulations we have calculated the average density of cooperators as a function of the temptation to defect. It is shown that the results obtained by numerical experiments depend strongly on the dynamics of the game, which could lower the important of scale-free topology on the persistence of the cooperation. Particularly, the system exhibits a phase transition, from active state (coexistence of cooperators and defectors) to absorbing state (only defectors surviving) when allowing `` worse\rq\rq strategy to be imitated in the evolution of the game.